How can I optimize a multiple (matrix) switch / case algorithm? - algorithm

Question

Is it possible to optimize this kind of (matrix) algorithm:
// | case 1 | case 2 | case 3 |
// ------|--------|--------|--------|
// | | | |
// case a| a1 | a2 | a3 |
// | | | |
// case b| b1 | b2 | b3 |
// | | | |
// case c| c1 | c2 | c3 |
// | | | |
switch (var)
{
case 1:
switch (subvar)
{
case a:
process a1;
case b:
process b1;
case c:
process c1;
}
case 2:
switch (subvar)
{
case a:
process a2;
case b:
process b2;
case c:
process c2;
}
case 3:
switch (subvar)
{
case a:
process a3;
case b:
process b3;
case c:
process c3;
}
}
The code is fairly simple but you have to imagine more complex with more "switch / case".
I work with 3 variables. According they take the values 1, 2, 3 or a, b, c or alpha, beta, charlie have different processes to achieve. Is it possible to optimize it any other way than through a series of "switch / case?
(Question already asked in french here).
Edit: (from Dran Dane's responses to comments below. These might as well be in this more prominent place!)
"optimize" is to be understood in terms of having to write less code, fewer "switch / case". The idea is to improve readability, maintainability, not performance.
There is maybe a way to write less code via a "Chain of Responsibility" but this solution is not optimal on all points, because it requires the creation of many objects in memory.

Answer 1

It sounds like what you want is a 'Finite State Machine' where using those cases you can activate different processes or 'states'. In C this is usually done with an array (matrix) of function pointers.
So you essentially make an array and put the right function pointers at the right indicies and then you use your 'var' as an index to the right 'process' and then you call it. You can do this in most languages. That way different inputs to the machine activate different processes and bring it to different states. This is very useful for numerous applications; I myself use it all of the time in MCU development.
Edit: Valya pointed out that I probably should show a basic model:
stateMachine[var1][var2](); // calls the right 'process' for input var1, var2

Answer 2

There are no good answers to this question :-(
because so much of the response depends on
The effective goals (what is meant by "optimize", what is unpleasing about the nested switches)
The context in which this construct is going to be applied (what are the ultimate needs implicit to the application)
TokenMacGuy was wise to ask about the goals. I took the time to check the question and its replies on the French site and I'm still puzzled as to the goals... Dran Dane latest response seems to point towards lessening the amount of code / improving readability but let's review for sure:
Processing Speed: not an issue the nested switches are quite efficient, possibly a tat less than 3 multiplications to get an index into a map table, but maybe not even.
Readability: yes possibly an issue, As the number of variables and level increases the combinatorial explosion kicks in, and also the format of the switch statement tends to spread the branching spot and associated values over a long vertical stretch. In this case a 3 dimension (or more) table initialized with fct. pointers puts back together the branching values and the function to be call on on a single line.
Writing less code: Sorry not much help here; at the end of the day we need to account for a relatively high number of combinations and the "map", whatever its form, must be written somewhere. Code generators such as TokenMacGuy's may come handy, it does seem a bit of an overkill in this case. Generators have their place, but I'm not sure it is the case here. One of two case: if the number of variables and level is small enough, the generator is not worth it (takes more time to set it up than to write the actual code in the first place), if the number of variables and levels is significant, the generated code is hard to read, hard to maintain...)
In a nutshell, my recommendation with regards to making the code more readable (and a bit faster to write) is the table/matrix approach described on the French site.
This solution is in two part:
a one time initialization of a 3 dimensional array (for 3 levels); (or a "fancier" container structure if preferred: a tree for example) . This is done with code like:
// This is positively more compact / readable
...
FctMap[1][4][0] = fctAlphaOne;
FctMap[1][4][1] = fctAlphaOne;
..
FctMap[3][0][0] = fctBravoCharlie4;
FctMap[3][0][1] = NULL; // impossible case
FctMap[3][0][2] = fctBravoCharlie4; // note how the same fct may serve in mult. places
And a relatively simple snippet wherever the functions need to be called:
if (FctMap[cond1][cond2][cond3]) {
retVal = FctMap[cond1][cond2][cond3](Arg1, Arg2);
if (retVal < 0)
DoSomething(); // anyway we're leveraging the common api to these fct not the switch alternative ....
}
A case which may prompt one NOT using the solution above are if the combination space is relatively sparsely populated (many "branches" in the switch "tree" are not used) or if some of the functions require a different set of parameters; For both of these cases, I'd like to plug a solution Joel Goodwin proposed first here, and which essentially combines the various keys for the several level into one longer key (with separator character if need be), essentially flattening the problem back to a long, but single level switch statement.
Now...
The real discussion should be about why we need such a mapping/decision-tree in the first place. To answer this unfortunately requires understanding the true nature of the underlying application. To be sure I'm not saying that this is indicative of bad design. A big dispatching section may make sense in some applications. However, even with the C language (which the French Site contributors seemed to disqualify to Object Oriented design), it is possible to adopt Object oriented methodology and patterns. Anyway I'm diverging...) It is possible that the application would overall be better served with alternative design patterns where the "information tree about what to call when" has been distributed in several modules and/or several objects.
Apologies to speak about this in rather abstract terms, it's just the lack of application specifics... The point remains: challenge the idea that we need this big dispatching tree; think of alternative approaches to the application at large.
Alors, bonne chance! ;-)

Answer 3

Depending on the language, some form of hash map with the pair (var, subvar) as the key and first-class functions as the values (or whatever your language offers to best approximate that, e.g. instances of classes extending some proper interface in Java) is likely to provide top performance -- and the utter conciseness of fetching the appropriate function (or whatever;-) from the map based on the key, and executing it, leads to high readability for readers familiar with the language and such functional idioms.

Answer 4

The idea of a function pointer is probably best (as per mjv, Shhnap). But, if the code under each case is fairly small, it may be overkill and result in more obfuscation than intended. In that case, I might implement something snappy and fast-to-read like this:
string decision = var1.ToString() + var2.ToString() + var3.ToString();
switch(decision)
{
case "1aa":
....
case "1ab":
....
}
Unfamiliar with your particular scenario so perhaps the previous suggestions are more appropriate.

Answer 5

I had exactly the same problem once, albeit for an immanent mess of a 5-parameter nested switch. I figured, why type all these O(N5) cases myself, why even invent 'nested' function names if the compiler can do this for me. And all this resulted in a 'nested specialized template switch' referring to a 'specialized template database'.
It's a little complicated to write. But I found it worth it: it results in a 'knowledge' database that is very easy to maintain, to debug, to add to etc... And I must admit: a sense of pride.
// the return type: might be an object actually _doing_ something
struct Result {
const char* value;
Result(): value(NULL){}
Result( const char* p ):value(p){};
};
Some variable types for switching:
// types used:
struct A { enum e { a1, a2, a3 }; };
struct B { enum e { b1, b2 }; };
struct C { enum e { c1, c2 }; };
A 'forward declaration' of the knowledge base: the 'api' of the nested switch.
// template database declaration (and default value - omit if not needed)
// specializations may execute code in stead of returning values...
template< A::e, B::e, C::e > Result valuedb() { return "not defined"; };
The actual switching logic (condensed)
// template layer 1: work away the first parameter, then the next, ...
struct Switch {
static Result value( A::e a, B::e b, C::e c ) {
switch( a ) {
case A::a1: return SwitchA<A::a1>::value( b, c );
case A::a2: return SwitchA<A::a2>::value( b, c );
case A::a3: return SwitchA<A::a3>::value( b, c );
default: return Result();
}
}
template< A::e a > struct SwitchA {
static Result value( B::e b, C::e c ) {
switch( b ) {
case B::b1: return SwitchB<a, B::b1>::value( c );
case B::b2: return SwitchB<a, B::b2>::value( c );
default: return Result();
}
}
template< A::e a, B::e b > struct SwitchB {
static Result value( C::e c ) {
switch( c ) {
case C::c1: return valuedb< a, b, C::c1 >();
case C::c2: return valuedb< a, b, C::c2 >();
default: return Result();
}
};
};
};
};
And the knowledge base itself
// the template database
//
template<> Result valuedb<A::a1, B::b1, C::c1 >() { return "a1b1c1"; }
template<> Result valuedb<A::a1, B::b2, C::c2 >() { return "a1b2c2"; }
This is how it can be used.
int main()
{
// usage:
Result r = Switch::value( A::a1, B::b2, C::c2 );
return 0;
}

Answer 6

Yes, there is definitely easier way to do that, both faster and simpler. The idea is basically the same as proposed by Alex Martelli. Instead of seeing you problem as bi-dimentional, see it as some one dimension lookup table.
It means combining var, subvar, subsubvar, etc to get one unique key and use it as your lookup table entry point.
The way to do it depends on the used language. With python combining var, subvar etc. to build a tuple and use it as key in a dictionnary is enough.
With C or such it's usually simpler to convert each keys to enums, then combine them using logical operators to get just one number that you can use in your switch (that's also an easy way to use switch instead of string comparizons with cascading ifs). You also get another benefit doing it. It's quite usual that several treatments in different branches of the initial switch are the same. With the initial form it's quite difficult to make that obvious. You'll probably have some calls to the same functions but it's at differents points in code. Now you can just group the identical cases when writing the switch.
I used such transformation several times in production code and it's easy to do and to maintain.
Summarily you can get something like this... the mix function obviously depends on your application specifics.
switch (mix(var, subvar))
{
case a1:
process a1;
case b1:
process b1;
case c1:
process c1;
case a2:
process a2;
case b2:
process b2;
case c2:
process c2;
case a3:
process a3;
case b3:
process b3;
case c3:
process c3;
}

Answer 7

Perhaps what you want is code generation?
#! /usr/bin/python
first = [1, 2, 3]
second = ['a', 'b', 'c']
def emit(first, second):
result = "switch (var)\n{\n"
for f in first:
result += " case {0}:\n switch (subvar)\n {{\n".format(f)
for s in second:
result += " case {1}:\n process {1}{0};\n".format(f,s)
result += " }\n"
result += "}\n"
return result
print emit(first,second)
#file("autogen.c","w").write(emit(first,second))
This is pretty hard to read, of course, and you might really want a nicer template language to do your dirty work, but this will ease some parts of your task.

Answer 8

If C++ is an option i would try using virtual function and maybe double dispatch. That could make it much cleaner. But it will only probably pay off only if you have many more cases.
This article on DDJ.com might be a good entry.

Answer 9

If you're just trying to eliminate the two-level switch/case statements (and save some vertical space), you can encode the two variable values into a single value, then switch on it:
// Assumes var is in [1,3] and subvar in [1,3]
// and that var and subvar can be cast to int values
switch (10*var + subvar)
{
case 10+1:
process a1;
case 10+2:
process b1;
case 10+3:
process c1;
//
case 20+1:
process a2;
case 20+2:
process b2;
case 20+3:
process c2;
//
case 30+1:
process a3;
case 30+2:
process b3;
case 30+3:
process c3;
//
default:
process error;
}

Answer 10

If your language is C#, and your choices are short enough and contain no special characters you can use reflection and do it with just a few lines of code. This way, instead of manually creating and maintaining an array of function pointers, use one that the framework provides!
Like this:
using System.Reflection;
...
void DispatchCall(string var, string subvar)
{
string functionName="Func_"+var+"_"+subvar;
MethodInfo m=this.GetType().GetMethod(fName);
if (m == null) throw new ArgumentException("Invalid function name "+ functionName);
m.Invoke(this, new object[] { /* put parameters here if needed */ });
}
void Func_1_a()
{
//executed when var=1 and subvar=a
}
void Func_2_charlie()
{
//executed when var=2 and subvar=charlie
}

Answer 11

Solution from developpez.com
Yes, you can optimize it and make it so much cleaner. You can not use such a "Chain of
Responsibility" with a Factory:
public class ProcessFactory {
private ArrayList<Process> processses = null;
public ProcessFactory(){
super();
processses = new ArrayList<Process>();
processses.add(new ProcessC1());
processses.add(new ProcessC2());
processses.add(new ProcessC3());
processses.add(new ProcessC4());
processses.add(new ProcessC5(6));
processses.add(new ProcessC5(22));
}
public Process getProcess(int var, int subvar){
for(Process process : processses){
if(process.canDo(var, subvar)){
return process;
}
}
return null;
}
}
Then just as your processes implement an interface process with canXXX you can easily use:
new ProcessFactory().getProcess(var,subvar).launch();